FWIW, check the papers to see how the gun was registered. If it was registered under the serial number of the carbine, the carbine is the machinegun and has to be transferred as such.

But many M1 carbines were converted using a kit. If the kit was given an IRS number that was marked on a key part (like the disconnector lever), then the kit is the registered machinegun and can be moved from one M1 carbine to another at any time, and can be transferred without transferring the carbine.